Identifier
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Images
[(1,2)] => [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
[(1,2),(3,4)] => [2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
[(1,3),(2,4)] => [3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
[(1,4),(2,3)] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,9),(6,9),(7,11),(8,10),(9,10),(9,11),(10,12),(11,12)],13)
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,10),(9,10),(10,11)],12)
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,13),(3,12),(4,11),(5,11),(5,14),(6,12),(6,14),(8,10),(9,10),(10,7),(11,8),(12,9),(13,7),(14,8),(14,9)],15)
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,11),(9,12),(10,12),(11,9),(11,10)],13)
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,13),(5,14),(6,14),(8,7),(9,7),(10,8),(11,9),(12,8),(12,9),(13,10),(13,12),(14,11),(14,12)],15)
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,8),(6,8),(7,9),(8,10),(9,11),(10,11)],12)
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,12),(5,12),(5,13),(6,10),(6,11),(8,7),(9,7),(10,8),(11,8),(12,9),(13,9)],14)
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,10),(9,10),(10,11)],12)
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,13),(3,12),(4,11),(5,11),(5,14),(6,12),(6,14),(8,10),(9,10),(10,7),(11,8),(12,9),(13,7),(14,8),(14,9)],15)
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,8),(6,8),(7,9),(8,10),(9,11),(10,11)],12)
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(2,12),(3,13),(4,13),(5,11),(5,14),(6,10),(6,14),(8,7),(9,7),(10,8),(11,9),(12,10),(13,11),(14,8),(14,9)],15)
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,15),(2,14),(3,19),(3,21),(4,20),(4,21),(5,14),(5,19),(6,15),(6,20),(8,10),(9,11),(10,12),(11,13),(12,7),(13,7),(14,8),(15,9),(16,10),(16,18),(17,11),(17,18),(18,12),(18,13),(19,8),(19,16),(20,9),(20,17),(21,16),(21,17)],22)
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,14),(2,14),(3,15),(4,15),(5,17),(6,17),(7,18),(8,18),(10,13),(11,12),(12,9),(13,9),(14,11),(15,10),(16,12),(16,13),(17,11),(17,16),(18,10),(18,16)],19)
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,10),(4,10),(5,9),(6,9),(7,12),(8,12),(9,13),(10,14),(11,14),(12,13),(12,15),(13,16),(14,15),(15,16)],17)
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,19),(2,19),(3,17),(4,17),(5,16),(6,15),(7,15),(7,18),(8,16),(8,18),(10,13),(11,10),(12,10),(13,9),(14,9),(15,11),(16,12),(17,14),(18,11),(18,12),(19,13),(19,14)],20)
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,9),(6,9),(7,10),(8,10),(9,11),(10,12),(12,11)],13)
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,12),(3,10),(4,10),(5,9),(6,9),(7,11),(8,11),(9,15),(10,15),(11,14),(12,16),(13,16),(15,12),(15,13),(16,14)],17)
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,10),(6,10),(7,9),(8,9),(9,11),(10,11),(11,12)],13)
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,17),(2,17),(3,14),(4,14),(5,15),(6,15),(7,13),(8,12),(10,16),(11,16),(12,9),(13,9),(14,11),(15,10),(16,12),(16,13),(17,10),(17,11)],18)
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,12),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,15),(10,14),(11,14),(12,16),(13,16),(14,15),(15,12),(15,13)],17)
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,10),(6,10),(7,9),(8,9),(9,11),(10,11),(11,12)],13)
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,15),(2,15),(3,14),(4,13),(5,17),(6,17),(7,18),(8,18),(10,12),(11,12),(12,9),(13,10),(14,11),(15,9),(16,10),(16,11),(17,13),(17,16),(18,14),(18,16)],19)
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,12),(3,10),(4,10),(5,11),(6,11),(7,9),(8,9),(9,14),(10,12),(11,13),(12,15),(13,15),(15,14)],16)
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,14),(2,13),(3,16),(4,15),(5,17),(6,17),(7,15),(7,16),(8,13),(8,14),(10,12),(11,12),(12,9),(13,10),(14,10),(15,11),(16,11),(17,9)],18)
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,9),(8,9),(9,10),(11,10)],12)
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(2,10),(3,9),(4,9),(5,12),(6,12),(7,11),(8,11),(9,13),(10,13),(11,15),(12,14),(13,14),(13,15),(14,16),(15,16)],17)
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,16),(2,16),(3,17),(4,17),(5,15),(6,14),(7,14),(7,19),(8,15),(8,19),(10,18),(11,18),(12,9),(13,9),(14,10),(15,11),(16,13),(17,12),(18,12),(18,13),(19,10),(19,11)],20)
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,9),(6,9),(7,10),(8,10),(9,11),(10,12),(12,11)],13)
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,12),(3,10),(4,10),(5,11),(6,11),(7,9),(8,9),(9,14),(10,12),(11,13),(12,15),(13,15),(15,14)],16)
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,17),(2,17),(3,15),(4,15),(5,16),(6,16),(7,14),(7,18),(8,13),(8,18),(10,12),(11,12),(12,9),(13,10),(14,11),(15,13),(16,14),(17,9),(18,10),(18,11)],19)
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,15),(2,15),(3,15),(4,15),(5,10),(6,9),(7,9),(7,11),(8,10),(8,11),(9,12),(10,13),(11,12),(11,13),(12,14),(13,14),(14,15)],16)
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,14),(2,13),(3,16),(4,15),(5,17),(6,17),(7,15),(7,19),(8,16),(8,19),(10,12),(11,12),(12,18),(13,9),(14,9),(15,10),(16,11),(17,18),(18,13),(18,14),(19,10),(19,11)],20)
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,13),(3,13),(4,13),(5,11),(6,10),(7,9),(8,9),(9,13),(10,12),(11,12),(13,10),(13,11)],14)
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,12),(10,12),(11,12)],13)
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,12),(10,12),(11,12)],13)
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,9),(6,9),(7,10),(8,10),(9,11),(10,12),(12,11)],13)
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,12),(3,10),(4,10),(5,9),(6,9),(7,11),(8,11),(9,15),(10,15),(11,14),(12,16),(13,16),(15,12),(15,13),(16,14)],17)
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,10),(6,10),(7,9),(8,9),(9,11),(10,11),(11,12)],13)
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,11),(10,11)],12)
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(2,10),(3,9),(4,9),(5,12),(6,12),(7,11),(8,11),(9,13),(10,13),(11,15),(12,14),(13,14),(13,15),(14,16),(15,16)],17)
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,17),(2,17),(3,16),(4,16),(5,15),(6,14),(7,14),(7,20),(8,15),(8,21),(10,12),(11,13),(12,9),(13,9),(14,10),(15,11),(16,19),(17,19),(18,12),(18,13),(19,20),(19,21),(20,10),(20,18),(21,11),(21,18)],22)
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,14),(2,14),(3,15),(4,15),(5,17),(6,17),(7,18),(8,18),(10,13),(11,12),(12,9),(13,9),(14,11),(15,10),(16,12),(16,13),(17,11),(17,16),(18,10),(18,16)],19)
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,10),(6,10),(7,10),(8,10),(10,9),(11,9)],12)
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,10),(4,10),(5,12),(6,11),(7,13),(8,14),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,10),(6,10),(7,9),(8,9),(9,11),(10,11),(11,12)],13)
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,15),(2,15),(3,14),(4,13),(5,17),(6,17),(7,18),(8,18),(10,12),(11,12),(12,9),(13,10),(14,11),(15,9),(16,10),(16,11),(17,13),(17,16),(18,14),(18,16)],19)
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,12),(3,10),(4,10),(5,11),(6,11),(7,9),(8,9),(9,14),(10,12),(11,13),(12,15),(13,15),(15,14)],16)
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,11),(10,11)],12)
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,12),(3,15),(4,14),(5,16),(6,16),(7,17),(8,17),(10,9),(11,9),(12,11),(13,11),(14,10),(15,10),(16,12),(16,13),(17,14),(17,15)],18)
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,10),(4,10),(5,12),(6,11),(7,13),(8,14),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,15),(2,14),(3,17),(4,16),(5,13),(6,12),(7,14),(7,15),(8,16),(8,17),(10,12),(11,13),(12,9),(13,9),(14,10),(15,10),(16,11),(17,11)],18)
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,14),(2,14),(3,15),(4,15),(5,13),(6,12),(7,17),(8,18),(10,9),(11,9),(12,10),(13,11),(14,17),(15,18),(16,10),(16,11),(17,12),(17,16),(18,13),(18,16)],19)
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,15),(2,14),(3,17),(4,16),(5,13),(6,12),(7,14),(7,15),(8,16),(8,17),(10,9),(11,9),(12,10),(13,11),(14,18),(15,18),(16,19),(17,19),(18,12),(18,20),(19,13),(19,20),(20,10),(20,11)],21)
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,10),(4,10),(5,12),(6,11),(7,13),(8,14),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,16),(2,16),(3,17),(4,17),(5,15),(6,14),(7,12),(7,14),(8,13),(8,15),(10,9),(11,9),(12,10),(13,11),(14,10),(15,11),(16,12),(17,13)],18)
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,17),(2,16),(3,19),(4,18),(5,16),(5,20),(6,17),(6,20),(7,18),(7,21),(8,19),(8,21),(10,15),(11,15),(12,14),(13,14),(14,9),(15,9),(16,10),(17,11),(18,12),(19,13),(20,10),(20,11),(21,12),(21,13)],22)
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,11),(10,11)],12)
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,11),(10,11)],12)
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,14),(2,13),(3,16),(4,15),(5,17),(6,17),(7,15),(7,16),(8,13),(8,14),(10,12),(11,12),(12,9),(13,10),(14,10),(15,11),(16,11),(17,9)],18)
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,9),(8,9),(9,10),(11,10)],12)
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,11),(10,11)],12)
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,11),(10,11)],12)
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,10),(8,9),(9,11),(10,11),(12,9),(12,10)],13)
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,12),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,15),(10,14),(11,14),(12,16),(13,16),(14,15),(15,12),(15,13)],17)
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,12),(10,12),(11,12)],13)
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,17),(2,17),(3,16),(4,16),(5,15),(6,14),(7,14),(7,18),(8,15),(8,18),(10,12),(11,12),(12,9),(13,9),(14,10),(15,11),(16,13),(17,13),(18,10),(18,11)],19)
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(2,10),(3,9),(4,9),(5,12),(6,12),(7,11),(8,11),(9,14),(10,14),(11,13),(12,13),(13,15),(14,15)],16)
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,10),(4,10),(5,9),(6,9),(7,12),(8,12),(9,13),(10,14),(11,14),(12,13),(12,15),(13,16),(14,15),(15,16)],17)
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,19),(2,19),(3,17),(4,17),(5,16),(6,15),(7,15),(7,18),(8,16),(8,18),(10,13),(11,10),(12,10),(13,9),(14,9),(15,11),(16,12),(17,14),(18,11),(18,12),(19,13),(19,14)],20)
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,17),(2,17),(3,16),(4,16),(5,15),(6,14),(7,14),(7,18),(8,15),(8,18),(10,12),(11,12),(12,9),(13,9),(14,10),(15,11),(16,13),(17,13),(18,10),(18,11)],19)
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,17),(2,16),(3,19),(4,18),(5,16),(5,20),(6,17),(6,20),(7,18),(7,21),(8,19),(8,21),(10,15),(11,15),(12,14),(13,14),(14,9),(15,9),(16,10),(17,11),(18,12),(19,13),(20,10),(20,11),(21,12),(21,13)],22)
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,11),(10,11)],12)
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,12),(10,12),(11,12)],13)
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,11),(10,11)],12)
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,14),(2,13),(3,16),(4,15),(5,17),(6,17),(7,15),(7,19),(8,16),(8,19),(10,12),(11,12),(12,18),(13,9),(14,9),(15,10),(16,11),(17,18),(18,13),(18,14),(19,10),(19,11)],20)
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,13),(3,13),(4,13),(5,11),(6,10),(7,9),(8,9),(9,13),(10,12),(11,12),(13,10),(13,11)],14)
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,12),(10,12),(11,12)],13)
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,12),(10,12),(11,12)],13)
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,9),(6,9),(7,10),(8,10),(9,11),(10,12),(12,11)],13)
>>> Load all 129 entries. <<<
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,12),(3,10),(4,10),(5,11),(6,11),(7,9),(8,9),(9,14),(10,12),(11,13),(12,15),(13,15),(15,14)],16)
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,11),(10,11)],12)
[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,16),(2,16),(3,17),(4,17),(5,15),(6,14),(7,12),(7,14),(8,13),(8,15),(10,9),(11,9),(12,10),(13,11),(14,10),(15,11),(16,12),(17,13)],18)
[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(2,10),(3,9),(4,9),(5,12),(6,12),(7,11),(8,11),(9,14),(10,14),(11,13),(12,13),(13,15),(14,15)],16)
[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,10),(6,10),(7,10),(8,10),(10,9),(11,9)],12)
[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,14),(2,14),(3,15),(4,15),(5,13),(6,12),(7,17),(8,18),(10,9),(11,9),(12,10),(13,11),(14,17),(15,18),(16,10),(16,11),(17,12),(17,16),(18,13),(18,16)],19)
[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,16),(2,16),(3,17),(4,17),(5,15),(6,14),(7,12),(7,18),(8,13),(8,18),(10,9),(11,9),(12,10),(13,11),(14,12),(15,13),(16,14),(17,15),(18,10),(18,11)],19)
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,17),(2,16),(3,19),(4,18),(5,18),(5,19),(6,16),(6,17),(7,14),(7,20),(8,15),(8,20),(10,14),(11,15),(12,9),(13,9),(14,12),(15,13),(16,10),(17,10),(18,11),(19,11),(20,12),(20,13)],21)
[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(2,9),(3,10),(4,10),(5,12),(6,11),(7,13),(8,14),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,12),(10,12),(11,12)],13)
[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,17),(2,17),(3,15),(4,15),(5,16),(6,16),(7,14),(7,18),(8,13),(8,18),(10,12),(11,12),(12,9),(13,10),(14,11),(15,13),(16,14),(17,9),(18,10),(18,11)],19)
[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,15),(2,15),(3,15),(4,15),(5,10),(6,9),(7,9),(7,11),(8,10),(8,11),(9,12),(10,13),(11,12),(11,13),(12,14),(13,14),(14,15)],16)
[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,12),(10,12),(11,12)],13)
[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,15),(2,14),(3,17),(4,16),(5,13),(6,12),(7,14),(7,15),(8,16),(8,17),(10,12),(11,13),(12,9),(13,9),(14,10),(15,10),(16,11),(17,11)],18)
[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,16),(2,16),(3,17),(4,17),(5,15),(6,14),(7,12),(7,18),(8,13),(8,18),(10,9),(11,9),(12,10),(13,11),(14,12),(15,13),(16,14),(17,15),(18,10),(18,11)],19)
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [6,3,2,5,4,1,8,7,10,9] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,17),(2,17),(3,21),(4,21),(5,19),(6,19),(7,18),(8,18),(9,16),(10,15),(12,14),(13,11),(14,11),(15,12),(16,12),(17,13),(18,20),(19,20),(20,15),(20,16),(21,13),(21,14)],22)
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [8,3,2,5,4,7,6,1,10,9] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,19),(2,19),(3,21),(4,21),(5,17),(6,17),(7,18),(8,18),(9,16),(10,15),(12,20),(13,20),(14,11),(15,14),(16,14),(17,13),(18,12),(19,11),(20,15),(20,16),(21,12),(21,13)],22)
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,8,5,4,7,6,3,10,9] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,16),(2,16),(3,17),(4,17),(5,19),(6,19),(7,18),(8,18),(9,15),(10,14),(12,11),(13,11),(14,21),(15,21),(16,13),(17,12),(18,20),(19,20),(20,14),(20,15),(21,12),(21,13)],22)
[(1,10),(2,7),(3,4),(5,6),(8,9)] => [10,7,4,3,6,5,2,9,8,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,14),(2,13),(3,16),(4,15),(5,18),(6,18),(7,17),(8,17),(9,19),(10,19),(12,21),(13,12),(14,12),(15,11),(16,11),(17,20),(18,20),(19,21),(20,13),(20,14),(21,15),(21,16)],22)
[(1,2),(3,10),(4,5),(6,7),(8,9)] => [2,1,10,5,4,7,6,9,8,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,19),(2,19),(3,21),(4,21),(5,17),(6,17),(7,18),(8,18),(9,16),(10,15),(12,20),(13,20),(14,11),(15,14),(16,14),(17,13),(18,12),(19,11),(20,15),(20,16),(21,12),(21,13)],22)
[(1,8),(2,9),(3,5),(4,6),(7,10)] => [8,9,5,6,3,4,10,1,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,16),(2,16),(3,12),(4,12),(5,11),(6,11),(7,14),(8,14),(9,13),(10,13),(11,15),(12,15),(13,16),(14,16),(15,16)],17)
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,10,7,6,9,8,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,17),(2,17),(3,21),(4,21),(5,19),(6,19),(7,18),(8,18),(9,16),(10,15),(12,14),(13,11),(14,11),(15,12),(16,12),(17,13),(18,20),(19,20),(20,15),(20,16),(21,13),(21,14)],22)
[(1,10),(2,3),(4,9),(5,6),(7,8)] => [10,3,2,9,6,5,8,7,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,14),(2,13),(3,16),(4,15),(5,18),(6,18),(7,17),(8,17),(9,19),(10,19),(12,21),(13,12),(14,12),(15,11),(16,11),(17,20),(18,20),(19,21),(20,13),(20,14),(21,15),(21,16)],22)
[(1,7),(2,3),(4,8),(5,9),(6,10)] => [7,3,2,8,9,10,1,4,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,18),(2,18),(3,12),(4,11),(5,14),(6,13),(7,15),(8,15),(9,13),(9,14),(10,11),(10,12),(11,16),(12,16),(13,17),(14,17),(15,18),(16,18),(17,18)],19)
[(1,8),(2,5),(3,4),(6,9),(7,10)] => [8,5,4,3,2,9,10,1,6,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,19),(2,19),(3,12),(4,11),(5,15),(6,15),(7,14),(8,14),(9,11),(9,13),(10,12),(10,13),(11,16),(12,17),(13,16),(13,17),(14,19),(15,19),(16,18),(17,18),(18,19)],20)
[(1,9),(2,7),(3,5),(4,10),(6,8)] => [9,7,5,10,3,8,2,6,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
lattice of intervals
Description
The lattice of intervals of a permutation.
An interval of a permutation $\pi$ is a possibly empty interval of values that appear in consecutive positions of $\pi$. The lattice of intervals of $\pi$ has as elements the intervals of $\pi$, ordered by set inclusion.